document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001645>Question 1001645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x - 3) is a factor of f(x) = x4 - 3x3 - 8x + 24. TRUE or FALSE\r<BR>\n" );
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document.write( "A rectangular fish tank with a square bottom whose height is half the length of its side contains 4000 cubic inches of water. what is the height of the fish tank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618828 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "(x - 3) is a factor of f(x) = x4 - 3x3 - 8x + 24. TRUE or FALSE?<BR>\n" );
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document.write( "TRUE.\r<BR>\n" );
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document.write( "It is TRUE because &nbsp;x=3 &nbsp;is the root of the polynomial &nbsp;f(x): &nbsp;&nbsp;f(3) = 0. &nbsp;&nbsp;(Check it !).\r<BR>\n" );
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document.write( "Use the &nbsp;<U>remainder theorem</U> &nbsp;(see the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial x-a</A>&nbsp; in this site).\r<BR>\n" );
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document.write( "A rectangular fish tank with a square bottom whose height is half the length of its side contains 4000 cubic inches \r<BR>\n" );
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document.write( "of water. What is the height of the fish tank?<BR>\n" );
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document.write( "Let &nbsp;x&nbsp; be the height of the fish tank.\r<BR>\n" );
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document.write( "Then its length is &nbsp;L = 2x &nbsp;and its width is &nbsp;W = 2x inches too, &nbsp;according to the condition. \r<BR>\n" );
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document.write( "(I assume that the tank is full, &nbsp;although you didn't mention it).\r<BR>\n" );
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document.write( "Hence, &nbsp;the water volume is &nbsp;V = L*W*H = (2x)*(2x)*x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3 ALIGN=MIDDLE  ALT=\"4x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;and you have an equation \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3 ALIGN=MIDDLE  ALT=\"4x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4000, &nbsp;&nbsp;&nbsp;&nbsp;or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1000.\r<BR>\n" );
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document.write( "The solution is &nbsp;x = 10 inches.\r<BR>\n" );
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document.write( "<U>Answer</U>. &nbsp;The height of the tank is &nbsp;10 inches.\r<BR>\n" );
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